NPBayes               package:NPBayes               R Documentation

_N_o_n_p_a_r_a_m_e_t_r_i_c _B_a_y_e_s _e_s_t_i_m_a_t_e _o_f _C_D_F _f_r_o_m _a_r_b_i_t_r_a_r_y _c_e_n_s_o_r_e_d _d_a_t_a

_D_e_s_c_r_i_p_t_i_o_n:

     This function will compute the nonparametric Bayes estimator of
     survival/distribution function from censored data with square
     error loss.  The prior is a Dirichlet process. 

     The data can be uncensored, right censored, left censored or
     interval censored, but must be nonnegative. We assume F(0)=0. 

     A left censored observation, t, is handled as an interval censored
     one with 'lefts' = 0; 'rights' = t.

_U_s_a_g_e:

     NPBayes(B, theta, u, uncen=numeric(0), rightcen=numeric(0),
               lefts=numeric(0), rights=numeric(0))

_A_r_g_u_m_e_n_t_s:

       B: a positive number. The parameter for the Dirichlet process
          prior.  The weight of prior information. If B is very small,
          then the resulting prior is "non-informative". 

   theta: a positive number. Another parameter for Dirichlet process
          prior.  The measure/parameter is  alpha [t, infty ) = B exp(
          - theta t) . 

       u: a non-negative number, where the Bayes estimator 1- hat F(u)
          is to be computed. 

   uncen: optional vector holding the uncensored observations. 

rightcen: optional vector holding the right censored observations. 

   lefts: optional vectors holding the left end-points of interval 
          censored observations. 

  rights: optional vectors holding the right end-points of interval 
          censored observations. Their length must agree. 

_D_e_t_a_i_l_s:

     If 'uncen', 'rightcen', 'lefts' and 'rights' are all missing, the
     estimator will be just the prior,  1-hat F(u) = exp(-theta u) . 

     The observations must all be non-negative.

     Due to rounding error and loss of significant digits in 
     subtraction, the result can be untrustworthy when  there are many
     interval censored data.

_V_a_l_u_e:

     a single value that is  the nonparametric Bayes estimator  1- hat
     F(u) .

_A_u_t_h_o_r(_s):

     Mai Zhou.

_R_e_f_e_r_e_n_c_e_s:

     Susarla and Van Ryzin (1976) Nonparametric Bayesian estimation of
     survival curves from incomplete observations. _ J. Amer. Statist.
     Assoc._ *71*,  897-902.

     Zhou, M. (2000). Nonparametric Bayes estimator of survival
     functions for doubly/interval censored data. Tech Report, Univ. of
     Kentucky.  

     See also Zhou, M. (2004). Statistica Sinica.

_E_x_a_m_p_l_e_s:

     uncensored <- c(1,5,9)
     rightcensored <- c(4,7)
     NPBayes(B=12, theta=0.2, u=3.2, uncen=uncensored, rightcen=rightcensored)

     leftpt <- 0
     rightpt <- 3
     NPBayes(B=12, theta=0.2, u=3.2, uncen=uncensored, rightcen=rightcensored, 
     lefts = leftpt, rights = rightpt)